MATHEMATICAL SECTION. 143 
Let a (= 6 feet) be the limiting value of « and b (= 3 feet) that 
for y, then we have, if n,, is the number of hitting shots 
a * b , 
dz a dy ST Se 
Eagles Te re NGI ease aN Ga 
% dz eee 9 z 72 
i => — 2 x = — dt ir 
The integral P#, f ie ‘ =) é , and 
similarly Pi,, is tabulated in Chauvenet’s Method of Least Squares 
(Table IX, appendix, to the argument ¢), and is therefore known. * 
We have further: 
ny a can b yy 
[a] Pals oe f is ee é 2e2? £ dy _ a ze? 
; Say 8/20 ane ey 20 
a x2 
oe 
= nPt, [Sse = 6 +), ss dives 
= ne, Pt, (Pt, — tP't,) (25,) 
2 
9 fete 
= 
Here P’t, denotes —+* fy mies e and can also be taken from 
Chauvenet’s table, £6 100 X difference. Similarly, 
1 
[y"] = ne,'Pt, (Ph — hP) (25,) 
By virtue of (24) we have also 
[a7] Nay 
ep Abi es / 
- P%. (25,’) 
nol 07) 
Talia 
hte ae (25,') 
wll 2, ) 
and these formule may be used to compute «, and «, by an obvious 
ab 
2 
approximative process. They show that «,* > a as it should 
‘ab 
